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If the equation of the plane passing through the line of intersection

If the equation of the plane passing through the line of intersection of the planes 2x – 7y + 4z... View Article

Let there be three independent events

Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is ɑ, only E2... View Article

The value of the limit

The value of limx→0+ [cos-1 (x – [x]2) . sin-1 (x – [x]2)] / [x – x3], where [x] denotes... View Article

The area of the triangle with vertices A (z), B (iz) and C (z + iz) is:

a. (1 / 2) |z + iz|2 b. 1 c. 1 / 2 d. (1 / 2) |z|2 Answer: (d)... View Article

In a school, there are three types of games to be played.

In a school, there are three types of games to be played. Some of the students play two types of... View Article

The inverse of y = 5^logx is

a. x = 5logy b. x= ylog5c. x = y1/log5 d. x = 51/logy Answer: (c) y = 5logx log5... View Article

Two dice are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is:

a. 17 / 36 b. 4 / 9 c. 5 / 12 d. 1/2 Answer: (a) n (S) = 36... View Article

If the fourth term in the expansion of (x + x^{log_{2} x})⁷is 4480, then the value of x where x ∈ N is equal to

a. 4 b. 3 c. 2 d. 1 Answer: (c) 7C3 x4 (xlog2 x)3 = 4480 35x4 (xlog2 x)3 =... View Article

If cot^-1 (ɑ) = cot^-12 + cot^-1 8 + cot^-118 + cot^-1 32 + …….. upto 100 terms, then ɑ is:

a. 1.03 b. 1.00 c. 1.01 d. 1.02 Answer: (c) RHS = ∑n=1100 cot-1 2n2 = ∑n=1100 tan-1 (2 /... View Article

In a triangle PQR, the coordinates of the points P and Q are (-2, 4) and (4, -2) respectively.

In a triangle PQR, the coordinates of the points P and Q are (-2, 4) and (4, -2) respectively. If... View Article

Team A consists of 7 boys and n girls and Team B has 4 boys and 6 girls.

Team A consists of 7 boys and n girls and Team B has 4 boys and 6 girls. If a... View Article

The line 2x – y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x – 2y = 4. Then, the radius of the circle is:

a. 4√5 b. 3√5 c. 5√3 d. 5√4 Answer: (b) m1 * m2 = – 1 [{[a – 4] /... View Article

If A = [latex]\begin{pmatrix} 0 &sin\alpha \\ sin\alpha &0 \end{pmatrix}[/latex] and det (A² – (1 / 2) I) = 0, then a possible value of ɑ is:

a. π / 6 b. π / 2 c. π / 3 d. π / 4 Answer: (d) \(\begin{array}{l}A^{2}=\begin{pmatrix} 0... View Article

The equation of the plane which contains the y-axis and passes through the point (1, 2, 3) is:

a. 3x + z = 6 b. 3x − z = 0 c. x + 3z = 10 d. x... View Article

Let [latex]\vec{a}=2i-3j+4k,\vec{b}=7i+j-6k[/latex]. If [latex]\vec{r}\times\vec{a}=\vec{r}\times\vec{b},\vec{r}.(i+2j+k)=-3,[/latex], then [latex]\vec{r}.(2i-3j+k)=[/latex] is equal to

a. 10 b. 13 c. 12 d. 8 Answer: (c) \(\begin{array}{l}\\\vec{a}=(2,-3,4),\vec{b}=(7,1,-6)\\ \vec{r}\times\vec{a}-\vec{r}\times\vec{b}=0\\ \vec{r}\times(\vec{a}-\vec{b})=0\\ \vec{r}=\lambda(\vec{a}-\vec{b})\\ \vec{r}=\lambda (-5i-4j+10k)\\ \vec{r}.(2,-3,1)=?\\ \text \ If... View Article

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